In order to cavitate, your suction pressure at the very lowest pressure point in the pump suction. In an AODD pump, this point is probably within the suction check valve itself. That point must be less than or equal to the vapour pressure during the suction stroke, such that instead of pulling liquid into the pump to fill the area behind the diaphragm, instead this volume is instantaneously filled with vapour which then collapses back to liquid as the suction stroke completes. All this does is rob you of some capacity, and makes a little noise. It is unlikely to damage your pump.
The vapour pressure of your petrol is less than 1 atm at 90 C- it is not boiling inside the tank. Accordingly a pulsation dampener with a bladder/diaphragm in it which is pressurized to a pressure ABOVE atmospheric pressure, will hold the bladder/diaphragm against its suction limit stop- it will not vary in volume and act as a pulse dampener at all.
An empty chamber-type pulsation dampener is just like it sounds: it is a stand pipe- a capped piece of pipe connected to a tee, containing a bit of noncondensible vapour at start-up, and mounted as close as possible to the pump's suction. It has no diaphragm or bladder to separate the gas from the liquid. On each discharge stroke, it will fill completely with liquid, compressing the vapour in the headspace a bit. During the suction stroke, instead of drawing liquid from the tank through a long pipe with lots of frictional loss, the pump will draw down this standpipe a bit. It must be sized so that one stroke's worth of volume does not take the level in the standpipe below the NPSHR of the pump. You don't buy these- you make them out of pipe fittings. A small port at the top of the standpipe will permit it to be re-filled with nitrogen or another inert gas periodically, as the gas will eventually dissolve in the flowing liquid and leave the system Because your fluid has a substantial vapour pressure though, that's not such a big deal- it merely means you should make the standpipe a little taller so it can fill with vapour rather than requiring an inert gas fill.